Related papers: Backlund transformations for many-body systems rel…
We begin by considering several properties commonly (but not universally) possessed by B\"acklund transformations between hyperbolic Monge-Amp\`ere equations: wavelike nature of the underlying equations, preservation of independent…
The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory…
In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit…
A deformation of the classical trigonometric BC(n) Sutherland system is derived via Hamiltonian reduction of the Heisenberg double of SU(2n). We apply a natural Poisson-Lie analogue of the Kazhdan-Kostant-Sternberg type reduction of the…
The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
New exact completely closed homogeneous Generalized Master Equations (GMEs), governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of s particles (s<N) selected from N>>1…
We newly apply the improved Batalin-Fradkin-Tyutin(BFT) Hamiltonian method to the O(3) nonlinear sigma model, and directly obtain the compact form of nontrivial first class Hamiltonian by introducing the BFT physical fields. Furthermore,…
It is shown that B\"acklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry…
Recently, Lembert, Gilson et al proposed a lucid and systematic approach to obtain bilinear B\"{a}cklund transformations and Lax pairs for constant-coefficient soliton equations based on the use of binary Bell polynomials. In this paper, we…
We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases…
In natural and social science, many events happened at different space-times may be closely correlated. Two events, A (Alice) and B (Bob) are defined as correlated if one event is determined by another, say, $B=\hat{f} A$ for suitable…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently…
We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a B\"acklund transformation and prove its basic properties: canonicity, commutativity and…
B\"acklund transformations (BTs) for ordinary differential equations (ODEs), and in particular for hierarchies of ODEs, are a topic of great current interest. Here we give an improved method of constructing BTs for hierarchies of ODEs. This…
We consider continuous and discrete Schr\"odinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schr\"odinger systems). Transformed and explicit solutions are constructed using our…
We present a novel method for including the impact of massive neutrinos in cold dark matter N-body simulations. Our approach is compatible with widely employed Newtonian N-body codes and relies on only three simple modifications. First, we…
A key feature of integrable systems is that they can be solved to obtain exact analytical solutions. We show how new models can be constructed through generalisations of some well known nonlinear partial differential equations with…